I broadly agree agree, but the exam is zero-sum, so when you say that we don't want to establish an adversarial relationship "beyond what the event requires", I'm vacuously on board, because the zero-sum nature of the event requires us to screw over the competition as much as much as we can get away with.
I'm in full agreement that taking an explosive seal from a clanless ninja probably is far more meaningful to them than it is us, but put another way, this means that taking an explosive seal from a clanless ninja should be disproportionately effective at impairing them. Combine this with not wanting to establish adversarial relationships and not wanting to come off as petty thieves and the solution seems to be we loot the seals and return them, plus some extras, after the event. If we didn't chip in extra seals, then we're still screwing them over for nothing, but chipping in an extra [Graham's number] seals would be better for them than winning the event, especially because explosive seals are so much harder for them to come by. Thus, in principle, somewhere between 0 and Graham's number, there should be a number of seals that allows us to foster a nonadversarial (cooperative, even) relationship while still achieving our goal of coming out ahead in a zero-sum event (and not coming off as petty thieves).
